@DavidP I'll keep a record of everything I have to manually copy over and then post it here once I've got it working. At the moment it looks like you need to copy the product, customer, address, and order tables and the image directory. Plus of course any other tables for third party modules that you still want to use, such as Amazon & eBay.
I have a clean url's module on my prestashop store (which has been an absolute nightmare and the cause of most of my problems), but thankfully all I have to do is replicate it into the built in thirty bees settings and all my urls will be the same. If you are going from non standard to clean urls then I guess you will have to setup 301 redirects for each one.
The other way Lesley suggested to migrate was to make a clone of your prestashop store, delete all the third party modules and then do the migration. That will save you having to manually copy over all the tables and will hopefully remove all the prestashop problems. I'm going to have a crack at the first option though as I would prefer a completely clean install of thirty bees.